Martha’s utility function is U (x, y) = min{x + 2y, 2x + y}. George’s utility function is U (x, y) = min{2x + 4y, 4x + 2y}. If George and Martha have the same income and face the same prices for the goods x and y, how much more George uses of good y compared to Martha? Explain.
To find out how much more of good y George uses compared to Martha, we need to compare the coefficients of y in their utility functions.
Martha’s utility function is U(x, y) = min{x + 2y, 2x + y}. The coefficient of y in the first term is 2, and in the second term is 1.
George’s utility function is U(x, y) = min{2x + 4y, 4x + 2y}. In the first term, the coefficient of y is 4, and in the second term is 2.
From the comparison, we can see that George values good y more than Martha does. The coefficient of y in George’s utility function is double the coefficient of y in Martha’s utility function.
Therefore, George uses twice as much of good y compared to Martha.